Nonuniform surface temperature

For bodies with nonuniform surface temperature distributions, iet depends not only on the conditions at the boundary layer edge but also on the distribution of the surface temperature upstream of the location being considered. 

Nonuniform Surface Temperature. The previous section was devoted to uniform-temperature plates. In practice, however, this ideal condition seldom occurs, and it is necessary to account for the effects of surface temperature variations along the plate on the local and average convective heat transfer rates. TTiis is required especially in the regions directly downstream of surface temperature discontinuities, e.g., at seams between dissimilar structural elements in poor thermal contact. These effects cannot be accounted for by merely utilizing heat transfer coefficients corresponding to a uniform surface temperature coupled with the local enthalpy or temperature potentials. Such an approach not only leads to serious errors in magnitude of the local heat flux, but can yield the wrong direction, i.e., whether the heat flow is into or out of the surface. 

Nonuniform Surface Temperature. Transformations (Eq. 6.76) are applicable to flows with nonuniform surface temperature provided a linear viscosity law is assumed (pp = constant). The flat-plate results given previously for constant Prr may be applied to a cone with the requirement that the surface boundary conditions be the same in terms of C,. For a flat plate, C, x, and for a cone, C, x3. Therefore, the flat-plate results must be modified in such a way that lengths in the x direction are replaced by x3 to obtain the cone results. For example, Eq. 6.66, which expresses the effect of a stepwise surface temperature for a flat plate, becomes for a cone... 

The term on the right side of Eq. 6.118 has been added to account for a nonuniform surface temperature. 

Nonuniform Surface Temperature. Nonuniform surface temperatures affect the convective heat transfer in a turbulent boundary layer similarly as in a laminar case except that the turbulent boundary layer responds in shorter downstream distances The heat transfer to surfaces with arbitrary temperature variations is obtained by superposition of solutions for convective heating to a uniform-temperature surface preceded by a surface at the recovery temperature of the fluid (Eq. 6.65). For the superposition to be valid, it is necessary that the energy equation be linear in T or i, which imposes restrictions on the types of fluid property variations that are permitted. In the turbulent boundary layer, it is generally required that the fluid properties remain constant however, under the assumption that boundary layer velocity distributions are expressible in terms of the local stream function rather than y for ideal gases, the energy equation is also linear in T [%]. 

The thermal parameters for comfort should be relatively uniform both spatially and temporally. Variations in heat flow from the body make the physiological temperature regulation more difficult. Nonuniform thermal conditions can lead to nonuniform skin temperatures. The active elements of the regulatory system may need to make more adjustments and work harder in order to keep thermal skin and body temperatures stable. To avoid discomfort from environmental nonuniformities, the temperature difference between feet and head should be less than about 3 °C (Fig. 5.9) and the mean surface temperature or radiant difference from one side of the body to the other should not he greater then about 10 °C. 

Mean radiant The theoretical uniform surface temperature of an enclosure in which an occupant would exchange the same amount of radiant heat as in the actual nonuniform enclosure. 

Gr/v Re = 9.6) without causing recirculation, and thus nonuniform surface flux. Since the disk temperature is fixed in this simulation, a smaller value of the mixed-convection parameter corresponds to a larger value of the disk spin rate. 

A helical baffle bundle built in this w produces two distinct flow regions. The area outside of the adjacent baffle contact diameter tends to produce a stable helical cross flow. However, inside the diameter where adjacent baffles touch is a second region where vortical flow is induced but in which the intensity of the rotational component tends to decrease as one approaches the center of the bundle. For a fixed flow rate and helix angle, this tendency may be minimized by the proper selection of the baffle contact diameter. With the correct selection, stream temperatures may be made to be close to uniform across the bundle cross section through the shell. However, below a critical velocity (for the baffle configuration and fluid state), the tendency for nonuniformity of temperatures increases as velocity decreases until ever-increasing portions of the central core surface area pinch out with respect to temperature and become ineffective for further heat transfer. 

Figure 6-7. Three configurations for the shallow-cavity problem (a) Four isothermal solid walls with motion driven by tangential motion of the lower wall (b) the same problem as (a) except, in this case, the upper surface is an interface that may deform because of the flow (c) the configuration is the same as (b), except, in this case, the lower wall is stationary and the motion in the cavity is assumed to be driven by Marangoni stresses caused by nonuniform interface temperature that is due to the fact that the end walls are at different temperatures.

We see that the Ts depends on the rate of heat release q and that the overall effect of convection is to reduce the surface temperature and make it nonuniform, with the surface temperature being highest at q = 1 (i.e., the downstream stagnation point of the sphere) and lower at the front, q = — 1. The asymmetry is due to the fact that the radial temperature gradient is slightly increased at the front relative to the back and thus requires a slightly lower surface temperature to sustain the heat flux q, compared with the surface temperature that is required at the back. 

Uniform Surface Injection. Although a mass transfer distribution yielding a uniform surface temperature is most efficient, it is much easier to construct a porous surface with a uniform mass transfer distribution. Libby and Chen [34] have considered the effects of uniform foreign gas injection on the temperature distribution of a porous flat plate. For these conditions, however, boundary layer similarity does not hold. Libby and Chen extended the work of Iglisch [35] and Lew and Fanucci [36], where direct numerical solutions of the partial differential equations were employed. An example of the nonuniform surface enthalpy and coolant concentrations resulting from these calculations is shown in Fig. 6.16. 

This technique is very simple and of low cost. However, only the average heat flux over the entire solid is determined. It also relies on an accurate value of the target emissivity. It has only limited practical relevance and it is limited by the permissible maximum material temperature level of the solid. Also, the solid should be uniformly heated to obtain an accurate average measurement. Nonuniform heating complicates the energy balance calculations. In Kilham s studies [17,18], the cylinders were rotated to minimize surface temperature gradients. However, only a single thermocouple, mounted on the inside diameter of the hollow cylinder to measure the inside cylinder temperature, was used to calculate the surface temperature. 

Figure 1. Uniform surface model prediction of temperature programmed desorption data from a nonuniform surface for reactant A of Scheme I requires low values of desorption parameters (Aj = 3.22 X 10 s , Ej = 9.01 kcal mol") to capture peak breadth.

Figure 2. Uniform surface model prediction of temperature programmed desorption data from a nonuniform surface for A and C of Scheme I.

Desorption of species A and B due to the decomposition of species C appears in two states in both the nonuniform surface observations and the uniform surface predictions using the parameters of Table 2. Note that only species A is shown, as the desorption of species B is kinetically identical (see Table 1). Therefore, all observations made below for species A are equally valid for the adsorption and desorption of B. The high temperature state, centered at approximately 370-380 K, resembles in both shape and position the result of the TPD of species A shown above in Figure 1. This feature is ascribed to the desorption of species A from the surface with the occurrence of significant readsorption events. The low temperature feature, centered at 280 K in the nonuniform surface observation and 260 K in the uniform surface... 

The manufacture of thick composites is difficult because the internal temperature of the thick section lags behind the surface temperature. If the surface cures faster than the interior regions, resin can be trapped in the interior, which leads to nonuniform composition and voids. Another problem is thermal spiking, during which the heat produced in the interior cannot escape and therefore builds up. The autocatalytic nature of the curing process can lead to thermal runaway and nonuniform composition. Very slow heating rates can solve this problem, but at the expense of increased processing time. 

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